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Yes, but if a side can hire a rationalist to argue their case before the judge, then that rationalist will degenerate into a lawyer. (And how could you forbid assistance in arguments, precisely? Offline assistance at least will always be present.)
And since the lawyer-like rationalists can be paid as much as the richest party can afford, while the arbiter's fees are probably capped (so that anyone can ask for arbitration), the market will select the best performing lawyers and reward them with the greatest fees, and the best rationalists who seek money (which is such a cliched rational thing to do :-) will prefer being lawyers and not judges.
Edit: added: the market will also select the judges who are least swayed by lawyers. It still needs to be shown that the market will have good information as to whether a judge had decided because the real rational evidence leaned one way, or because a smart lawyer had spun it appropriately. It's not clear to me what this will collapse to, or whether there's one inevitable outcome at all.
Would a lawyer by any other name still speak bullshit? Yes. But why are we talking about lawyers and judges?
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